A small town has 300 people, all of whom are interested only in private consumption and in the quality of the city streets. The utility function of person i is given by U(X,, G) = X, + AG - B.G', where X, is the amount of money that person i has to spend on private goods and G is the amount of money that the town spends on fixing its streets. There are 3 types of people, and each type has 100 people. The parameters in their utility function is given by Type A B 0.5 09 19 P 0.5 10 1 (a) Find the absolute value of the marginal rate of substitution between public goods (spending on streets) and private goods for person i for each type. (Hint: visualize the indifference curve between public goods (G) and private goods (X,), in which G is on the horizontal axis and X, is on the vertical axis.) (b) How much spending on streets is socially optimal